CRUSHING AND GRINDING 217 adjacent particles, which never happens, or fracture takes place along a few surfaces by the breaking down of some of the weaker bonds, and the new particles thus formed are free to resume their original shape in-so-far as they are not held between the machine surfaces. The energy given up by them is probably used in some sort of lever action in making fracture planes. So the energy absorbed according to Kick's law does not stay in the particle after pressure is released and; therefore, this law does not govern to any great extent the amount of energy absorbed in crushing. Reference to Fig. 13 will explain how Rittinger's law applies. Supposing that it were possible to hold similar cubes between the two offset faces as shown and that v| 1 D D(To break) D (To break) FIG. 13.-100-mesh cube -Rittinger's law. 200-mesh cube Area one section = A Area one section • Average resistance to shear per square inch : Eneregy =FAD Energy = F—D 4 F Surface produced = 2A Surface produced = 2~ .'. Energy pro portional to surface. forces were applied until the deformation shown by the dotted lines was obtained, it will be seen that only the molecules along the vertical center line are stressed and deformed, the mass of the cube away from this surface receiving practically no pressure or deformation. The energy in this case required to produce rupture will be the product of the average resistance to shearing per square inch by the area along which rupture takes place, and by the distance the two offset faces move together. The average resistance to shearing is a variable quantity, as the deformation increases up 40 80 120 1QO 200 240 Z&O 320 Reciprocals of DigmeiersCTheorelicalMeshj FIG. 14.—Crushing surface diagram. 360 to rupture. To reduce to cubes, this amount of energy must be multiplied by three, as three similar fracture planes must be made to produce cubes. And it will not be hard to see that the distance through which the offset faces must move in either case must be the same and not proportional to the thickness of the piece. To break the molecular bond between adjacent particles would require the same movement regardless of the thickness of the piece.